Problem: Solve for $x$ and $y$ using substitution. ${x-3y = 7}$ ${y = -4x-11}$
Explanation: Since $y$ has already been solved for, substitute $-4x-11$ for $y$ in the first equation. ${x - 3}{(-4x-11)}{= 7}$ Simplify and solve for $x$ $x+12x + 33 = 7$ $13x+33 = 7$ $13x+33{-33} = 7{-33}$ $13x = -26$ $\dfrac{13x}{{13}} = \dfrac{-26}{{13}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = -4x-11}\thinspace$ to find $y$ ${y = -4}{(-2)}{ - 11}$ $y = 8 - 11$ $y = -3$ You can also plug ${x = -2}$ into $\thinspace {x-3y = 7}\thinspace$ and get the same answer for $y$ : ${(-2)}{ - 3y = 7}$ ${y = -3}$